Definition 2.6 (see [[1]}, Definition 3.1 and 3.2] or [[2]}, Section 2.2.6])
Let \(\mathcal {F}\)  be a coherent sheaf on \(\mathcal {X}\) . Define the support of \(\mathcal {F}\) , denoted by \(\mathrm {Supp}(\mathcal {F})\) , to be the closed substack associated to the ideal \(\mathcal {I}\) :
\(0\rightarrow \mathcal {I}\rightarrow \mathcal {O}_{\mathcal {X}}\rightarrow \mathcal {E}nd_{\mathcal {O}_{\mathcal {X}}}(\mathcal {F}).\) 
